potential barrier

A potential barrier is a hump of high potential energy that a particle must somehow get past, like a hill standing between two valleys. To cross it classically, a particle needs at least as much energy as the height of the hump; with less, it rolls back down. Barriers appear everywhere in physics, from the repulsion that keeps two atoms apart to the wall of charge surrounding an atomic nucleus.

In the quantum world a barrier behaves very differently. A wave reaching a barrier taller than its energy does not stop dead at the edge. Instead the wavefunction decays exponentially as it pushes into the barrier, and if the barrier is thin enough, a small but nonzero piece of the wave emerges out the far side. The particle has, in effect, leaked through a wall it lacked the energy to climb — the phenomenon of tunnelling.

How much gets through depends sensitively on the barrier's height and, especially, its width. A wide or tall barrier kills the wave almost completely, while a thin one lets a measurable fraction through. This exquisite sensitivity is exactly what makes barrier-crossing useful: tiny changes in width produce huge changes in transmission, a leverage that scanning tunnelling microscopes turn into atomic-scale images of surfaces.